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Two point charge of \( 100 \mu \mathrm{C} \) and \( -4 \mu \mathrm{C} \) are positioned at points \( (-2 \sqrt{ } 3,3 \sqrt{ } 3,-4) \) and \( (4 \sqrt{ } 3,-5 \sqrt{3}, 6) \) respectively of a Cartesian coordinate system. Find the force vector on the \( -4 \mu \mathrm{C} \)
\( \mathrm{P} \) charge? All the coordinates are in meters.
(A) \( 9 \times 10^{-4}(3 \sqrt{3} \hat{i}-4 \sqrt{3} \hat{j}+5 \hat{k}) \)
(B) \( 9 \times 10^{-4}(-3 \sqrt{3} \hat{i}+4 \sqrt{3} \hat{j}-5 \hat{k}) \)
(C) \( 2.25 \times 10^{-4}(-3 \sqrt{3} \hat{i}+4 \sqrt{3} \hat{j}-5 \hat{k}) \)
(D) \( 2.25 \times 10^{-4}(3 \sqrt{3} \hat{i}-4 \sqrt{3} \hat{j}+5 \hat{k}) \)
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